Zipf's Law

In the English language, the probability of encountering the th most common word is given roughly by  for  up to 1000 or so. The law breaks down for less frequent words, since the harmonic series diverges. Pierce's (1980, p. 87) statement that  for  is incorrect. Goetz states the law as follows: The frequency of a word is inversely proportional to its statistical rank  such that

where  is the number of different words.

REFERENCES:

Bogomolny, A. "Benford's Law and Zipf's Law." https://www.cut-the-knot.org/do_you_know/zipfLaw.shtml.

Goetz, P. "Phil Goetz's Complexity Dictionary." https://www.cs.buffalo.edu/~goetz/dict.html

Li, W. "Zipf's Law." https://linkage.rockefeller.edu/wli/zipf/.

Pierce, J. R. Introduction to Information Theory: Symbols, Signals, and Noise, 2nd rev. ed. New York: Dover, pp. 86-87 and 238-239, 1980.